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Search: MSC category 57N10 ( Topology of general $3$-manifolds [See also 57Mxx] )

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1. CJM 2013 (vol 66 pp. 141)

Caillat-Gibert, Shanti; Matignon, Daniel
 Existence of Taut Foliations on Seifert Fibered Homology $3$-spheres This paper concerns the problem of existence of taut foliations among $3$-manifolds. Since the contribution of David Gabai, we know that closed $3$-manifolds with non-trivial second homology group admit a taut foliation. The essential part of this paper focuses on Seifert fibered homology $3$-spheres. The result is quite different if they are integral or rational but non-integral homology $3$-spheres. Concerning integral homology $3$-spheres, we can see that all but the $3$-sphere and the PoincarÃ© $3$-sphere admit a taut foliation. Concerning non-integral homology $3$-spheres, we prove there are infinitely many which admit a taut foliation, and infinitely many without taut foliation. Moreover, we show that the geometries do not determine the existence of taut foliations on non-integral Seifert fibered homology $3$-spheres. Keywords:homology 3-spheres, taut foliation, Seifert-fibered 3-manifoldsCategories:57M25, 57M50, 57N10, 57M15

2. CJM 2008 (vol 60 pp. 164)

Lee, Sangyop; Teragaito, Masakazu
 Boundary Structure of Hyperbolic $3$-Manifolds Admitting Annular and Toroidal Fillings at Large Distance For a hyperbolic $3$-manifold $M$ with a torus boundary component, all but finitely many Dehn fillings yield hyperbolic $3$-manifolds. In this paper, we will focus on the situation where $M$ has two exceptional Dehn fillings: an annular filling and a toroidal filling. For such a situation, Gordon gave an upper bound of $5$ for the distance between such slopes. Furthermore, the distance $4$ is realized only by two specific manifolds, and $5$ is realized by a single manifold. These manifolds all have a union of two tori as their boundaries. Also, there is a manifold with three tori as its boundary which realizes the distance $3$. We show that if the distance is $3$ then the boundary of the manifold consists of at most three tori. Keywords:Dehn filling, annular filling, toroidal filling, knotCategories:57M50, 57N10

3. CJM 2004 (vol 56 pp. 1022)

Matignon, D.; Sayari, N.
 Non-Orientable Surfaces and Dehn Surgeries Let $K$ be a knot in $S^3$. This paper is devoted to Dehn surgeries which create $3$-manifolds containing a closed non-orientable surface $\ch S$. We look at the slope ${p}/{q}$ of the surgery, the Euler characteristic $\chi(\ch S)$ of the surface and the intersection number $s$ between $\ch S$ and the core of the Dehn surgery. We prove that if $\chi(\hat S) \geq 15 - 3q$, then $s=1$. Furthermore, if $s=1$ then $q\leq 4-3\chi(\ch S)$ or $K$ is cabled and $q\leq 8-5\chi(\ch S)$. As consequence, if $K$ is hyperbolic and $\chi(\ch S)=-1$, then $q\leq 7$. Keywords:Non-orientable surface, Dehn surgery, Intersection graphsCategories:57M25, 57N10, 57M15